Modelling Feasible Design Regions Using Lattice‐based Kernel Methods

Abstract

AbstractReliability, robustness and general performance are key indicators when attempting to improve the design of existing engineering systems. The search for an improved design is conducted in the space of all possible designs, referred to as the design space. Often when searching this space, infeasible or unsafe regions are encountered, perhaps because particular combinations of parameter values are not physically possible. Such regions need to be avoided during optimization to ensure that any new design is itself feasible. In addition, when considering the reliability and robustness of a design, it may be important to know how far a feasible design is from any boundary. Indeed, it may be the case that such distances are directly related to the reliability and robustness of the design and it may, therefore, be useful to model the boundary between feasible and infeasible regions. This paper proposes the use of Hilbert bases as a method of identifying points in the design space that are close to, or on, the feasible boundary and then uses this information to model the boundary by defining positive definite kernels on new spaces such as hyperspheres. In this way it is possible to model whole surfaces as opposed to single functions. Copyright © 2004 John Wiley & Sons, Ltd.